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Question

In the given figure, ABCD is a parallelogram. Prove that AB=2BC
1159975_5d335f9ee6ac44749c2d62e56a81cfe9.png

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Solution

Let draw a line parallel to both lines BC and AD
now in AEOandADEAEAO=AEAD (by Thales's theorm)

AO=AD=BC

similarly inCBEandOBCEBBC=EBOB (by Thales's theorm)

OB=BCOA+OB=BC+BCAB=2BC
Proved

1045615_1159975_ans_1a1298113c36410fa75e891d397db29a.png

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